What Gaf is
Gaf (گ) is not one of the twenty-eight letters of the Arabic alphabet. It is one of four letters Persian added to the Arabic script in order to write sounds Arabic does not have, and it spread with the script into Persian, Urdu, Pashto, Kurdish and Turkic languages.
Classical Arabic has no hard g. It maps to ك, and Persian formed گ by adding a second stroke to ك.
How Ilm ul Huroof reads Gaf
It does not read it directly, and this is worth stating plainly. The Science of Letters was built on the twenty-eight Arabic letters, each tied to an element, a divine name and a numerical value in the abjad. The four Persian letters postdate that framework and have no classical reading of their own.
What the tradition does is read the Arabic base letter beneath the added dots. For Gaf, that base is Kaf (ك), and a name written with Gaf is read through Kaf's qualities and abjad value.
Anyone offering you a separate classical reading for Gaf is inventing it. We would rather tell you where the tradition stops.
Gaf in names
Names carrying Gaf are usually Persian, Turkic, Urdu or Pashto in origin rather than Arabic. On their AsrNaam pages the letter grid shows Gaf as written and reads it through Kaf.
Browse all letters, read the introduction to Ilm ul Huroof, or see why a name's Urdu spelling matters.
Gaf joins on both sides, so it takes all four shapes. In a word it connects to the letter before it and to the letter after it, and the shape you see depends on where in the word it falls.
Gaf is a moon letter. When the definite article ال (al-) comes before it, the l is pronounced clearly and stays audible, as in القمر, al-qamar, the moon, which gives this group its name. Names beginning with Gaf keep their al- intact when they carry one.